## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
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- Numerical Algebra, Control & Optimization
- Electronic Research Announcements
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- AIMS Mathematics

IPI

We derive some bounds which can be viewed as an evidence of increasing stability in the problem of recovering the potential coefficient in the Schrödinger equation from the Dirichlet-to-Neumann map in the presence of attenuation, when energy level/frequency is growing. These bounds
hold under certain a-priori regularity constraints on the unknown coefficient. Proofs use complex and bounded complex geometrical optics solutions.

IPI

We prove the unique continuation property for the isotropic elasticity system
with

*arbitrarily large*residual stress. This work improves the result obtained in [10] where the residual stress is assumed to be small.
DCDS

We study the local behavior of a solution to the
Stokes system with singular coefficients in $R^n$ with $n=2,3$. One
of our main results is a bound on the vanishing order of a
nontrivial solution $u$ satisfying the Stokes system, which is a
quantitative version of the strong unique continuation property for
$u$. Different from the previous known results, our strong unique
continuation result only involves the velocity field $u$. Our proof
relies on some delicate Carleman-type estimates. We first use these
estimates to derive crucial

*optimal*three-ball inequalities for $u$. Taking advantage of the optimality, we then derive an upper bound on the vanishing order of any nontrivial solution $u$ to the Stokes system from those three-ball inequalities. As an application, we derive a minimal decaying rate at infinity of any nontrivial $u$ satisfying the Stokes equation under some a priori assumptions.
IPI

We consider the reconstruction of obstacles inside a bounded
domain filled with an incompressible fluid. Our method relies on
special complex geometrical optics solutions for the stationary
Stokes equation with a variable viscosity.

## Year of publication

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